How to completely nullify rigid body bounciness
Probably better if you can attach your simplified blend with issue. Use https://blend-exchange.giantcowfilms.com and paste given code into your question. This topic is quite case sensitive :) and not always there is a solution.

Here with Cubes

Collisions &gt; Shape &gt; Box
Surface Response &gt; Friction &gt; 1 (Bounciness &gt; 0)
(probably also for small Cubes &gt; Dynamics &gt; Damping Translation &gt; 0)

Important - Apply Scale Ctrl+A to all objects.



Edit according to the given file:

You didn't set Collision Shape to Box.
Also one very important aspect is set Geometry to Origin for proper simulation. If collision box doesn't fit to your high-poly mesh, move vertices a bit closer to border in edit mode.

Sidenote - Is it OK to have object dimension just 4 mm? On my computer it starts flicker that can be fixed in 3Dview's side panel (N) &gt; View Clip Start = 1 mm End = 100 mm.
I'm asking because part of problems can be a size. Simulation on these micro values is not too much stable in general. But here works without bouncing with RB Active object &gt; Mass = 0.0001 mg and RB Passive object with Strength = -10000.